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GLOBAL SOLUTION OF A SEMILINEAR PARABOLIC EQUATION
Ding Xiaxi, Zhao Huijiang
Acta mathematica scientia,Series B. 1991, 11 (3):
254-266.
In this paper, we are concerned with the Cauchy problem: ut=△u+|u|γ-1u-u x∈Rn,γ>1,t∈R+ u(x,0)=u0(x) in Dqα. We got some existence and asymptotic results of their global solutions. Additionally, we got the global existence theorem of the Cauchy problem ut=△u+|u|γ-1u x∈Rn,γ>1,t∈R+ u(x,0)=u0(x) in Dqα, where q∈[(1)/2n(γ-1),∞),α=(2)/γ-1-(n)/q, in the case(1)/2n(γ-1)>1.
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